Solve for x and y : (1-2i)*x + (1+2i)*y = 1 + i

We'll note the complex number from the left side as z1 and
the complex number from the right side as z2.

For z1 = z2,
we'll have to impose the following conditions:

Re(z1) =
Re(z2)

Im(z1) = Im(z2)

To
determine the real and imaginar parts of the complex number from the left side, we'll
have to remove the brackets:

(1-2i)*x + (1+2i)*y = x - 2ix
+ y + 2iy

We'll combine the real parts and imaginary
parts:

Re(z1) = x+y

Im(z1) =
-2x + 2y

Re(z2) = 1

Im(z2) =
1

x+y = 1 (1)

-2x + 2y = 1
(2)

We'll multiply by 2
(1):

2x + 2y = 2 (3)

We'll add
(3) to (2):

2x + 2y - 2x + 2y =
2+1

We'll eliminate like
terms:

4y = 3

y
= 3/4

We'll substitute y in
(1):

x+y = 1

x + 3/4 =
1

x = 1 - 3/4

x =
(4-3)/4

x =
1/4